## The Regina Handbook |

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Copyright © 1999–2016 The Regina development team

Both Regina and this handbook are licensed under the terms of the GNU General Public License.

Regina is a software package for 3-manifold and 4-manifold topologists, with a focus on triangulations, normal surfaces and angle structures. For 3-manifolds, it includes high-level tasks such as 3-sphere recognition, connected sum decomposition and Hakenness testing, comes with a rich database of census manifolds, and incorporates the SnapPea kernel for working with hyperbolic manifolds. For 4-manifolds, it offers a range of combinatorial and algebraic tools, plus support for normal hypersurfaces. Regina comes with a full graphical user interface, as well as Python bindings and a low-level C++ programming interface.

This handbook is current as of 26 September 2016 for Regina 5.0.

Tip: You can also browse the alphabetical index of tasks.

**Table of Contents**

- 1. Introduction
- 2. Working with Packets
- 3. Triangulations
- Creation
- Analysis
- Identifying the Manifold (2-D and 3-D)
- Validity, Orientability and Other Basic Properties (All Dimensions)
- Viewing Facet Gluings (All Dimensions)
- Skeletal Information (All Dimensions)
- Algebraic Invariants (3-D and 4-D)
- Combinatorial Composition (3-D)
- High-Level Recognition Routines (3-D)
- SnapPea Calculations (3-D)
- Decomposition (All Dimensions)
- Triangulating Vertex Links (3-D and 4-D)
- Triangulating Boundary Components (4-D)

- Modification
- Editing Gluings (All Dimensions)
- Automatic Simplification (3-D and 4-D)
- Manual Simplification: Elementary Moves (3-D and 4-D)
- 0-Efficiency (3-D)
- Switching Between Real and Ideal (3-D and 4-D)
- Subdivision (3-D and 4-D)
- Orienting Triangulations and Double Covers (All Dimensions)
- Puncturing and Drilling (3-D)
- Building Connected Sums (3-D)
- Cutting Along and Crushing Normal Surfaces (3-D)

- 4. SnapPea Triangulations
- 5. Normal Surfaces and Hypersurfaces
- 6. Angle Structures
- 7. Importing and Exporting Data
- 8. Python Scripting
- 9. Configuration
- 10. Compiling Regina Into Your Projects
- 11. Troubleshooting and FAQ
- 12. Bug Tracking and Mailing Lists
- A. Command Line: Main Applications
- regina-gui - Regina's graphical user interface
- regina-python - Regina's command-line Python interface

- B. Command Line: Specialised Utilities
- censuslookup - Search for triangulations in Regina's census databases
- regconcat - Combine several Regina data files
- regconvert - Convert between different Regina file formats
- regfiledump - Dump the contents of a Regina data file
- regfiletype - Identify the formats of Regina data files
- sigcensus - Form a census of splitting surface signatures
- tricensus - Form a census of triangulations
- tricensus-mpi - Distribute a triangulation census amongst several machines using MPI
- tricensus-mpi-status - Summarise the log file of an MPI census of triangulations
- trisetcmp - Compare triangulations between two Regina data files

- C. Version History
- D. Authors and License
- Index
- Bibliography

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